We present a dynamic model of venture capital financing, described as a sequential investment problem with uncertain outcome. Each venture has to pass a sequence of milestones, and there is a chance of terminal failure in each milestone. The investors decide sequentially about the speed of the investment and, due to contract frictions and agency costs, will optimally structure investments in a discrete sequence of staged investments. We derive the dynamically optimal funding policy in response to the arrival of information during the development of the venture. We develop three types of predictions from our theoretical model and test these predictions in a large sample of venture capital investments in the U.S. for the period of 1987-2002. First, the investment flow starts low if the failure risk is high and accelerates as the projects mature. Second, the investment flow reacts positively to information that arrives while the project is developed. We find that the investment decisions are more sensitive to the information received during the development than to the information held prior to the project launch. Third, investors distribute their investments over more funding rounds if the failure risk is larger.